1. Field of the Invention
The invention relates generally to computer-aided electronic circuit simulation, and more particularly, to a method of extracting semiconductor device model parameters for use in integrated circuit simulation.
2. Description of Related Art
While the sizes of individual devices have decreased, the complexities of integrated circuits have increased at a dramatic rate over the past few decades. As circuits have become more complex, traditional breadboard methods have become burdensome and overly complicated. Modern circuit designers rely more and more on computer aids, and electronic circuit simulators have become indispensable tools for circuit design. Examples of electronic circuit simulators include the Simulation Program with Integrated Circuit Emphasis (SPICE) developed at the University of California, Berkeley (UC Berkeley), and various enhanced versions or derivatives of SPICE, such as, SPICE2 or SPICE3, also developed at UC Berkeley; HSPICE, developed by Meta-software and now owned by Avant!; PSPICE, developed by Micro-Sim; and SPECTRE, developed by Cadence, ELDO developed by Mentor Graphics, SSPICE developed by Silvaco, and the like. In addition, many semiconductor companies use their proprietary versions of SPICE circuit simulators. SPICE and its various versions or derivatives will be referred to hereafter as SPICE circuit simulators.
An electronic circuit may contain a variety of circuit elements such as resistors, capacitors, inductors, mutual inductors, transmission lines, diodes, bipolar junction transistors (BJT), junction field effect transistors (JFET), and metal-on-silicon field effect transistors (MOSFET), etc. A SPICE circuit simulator makes use of built-in or plug-in models for the circuit elements, especially semiconductor device elements (or device) such as diodes, BJTs, JFETs, and MOSFETs.
A model for a device mathematically represents the device characteristics under various bias conditions. For example, for a MOSFET device model, in DC and AC analysis, the inputs of the device model are the drain-to-source, gate-to-source, bulk-to-source voltages, and the device temperature. The outputs are the various terminal currents. A device model typically includes model equations and a set of model parameters. The set of model parameters for a semiconductor device is often referred as a model card (or, in abbreviation, a “model”) for the device. Together with the model equations, the model card directly affects the final outcome of the terminal currents and is used to emulate the behavior of the semiconductor device in an integrated circuit. In order to represent actual device performance, a successful device model is tied to the actual fabrication process used to manufacture the device represented. This connection is also represented by the model card, which is dependent on the fabrication process used to manufacture the device.
In modern device models, such as BSIM (Berkeley Short-Channel IGFET Model) and its derivatives, BSIM3, BSIM4, and BSIMPD (Berkeley Short-Channel IGFET Model Partial Depletion), all developed at UC Berkeley, only a few of the model parameters in a model card can be directly measured from actual devices. The rest of the model parameters are extracted using nonlinear equations with complex extraction methods. See Daniel Foty, “MOSFET Modeling with Spice—Principles and Practice,” Prentice Hall PTR, 1997.
Since simulation algorithms and convergence techniques in circuit simulators have become mature, the accuracy of SPICE simulation is mainly determined by the accuracy of the device models. As a result, there is a strong need for accurate device models to predict circuit performance. Traditionally, in an integrated circuit design, only MOSFETs having a single drawn channel length are utilized so that a single MOSFET model card, which is accurate for a single drawn channel length, would be sufficient. In modern integrated circuit design, however, it is not uncommon to include in an integrated circuit MOSFETs having different geometries, i.e., different drawn channel lengths and drawn channel widths. In addition to describing a set of devices with different geometries, a device model should also satisfy criteria outside the device's allowed operating regime to ensure robust convergence properties during circuit simulation. Furthermore, it is desirable that the device model should include the effect of device size fluctuations and technology modifications so that it can be used by circuit designers to study the statistical behavior of the circuits, and to explore circuit design for a modified or more advanced technology.
Before scalable models were developed, binning was used to expand the single device model cards to comprehend a broader range of device geometrical variations. When modeling MOSFET devices using binning, a geometrical space constituted by ranges of interest for the channel length and width is divided into smaller regions or bins, and a different binning model card is created for each of these bins. Although the binning model cards, when properly created, can accurately model device behavior in a broad range of device sizes, it is less scalable and involves many additional parameters that have no physical meanings. Also, to obtain the binning model cards with good accuracy, test results from many differently sized devices are required. Most importantly, since each binning model is created for its own bin in isolation from the creation of the binning models for the other bins, binning can result in discontinuity in device characteristics as the device geometry is varied across the boundaries of adjacent bins. This discontinuity can complicate statistical analysis of device and circuit behavior and cause convergence problem during circuit simulation.
To overcome the problems of binning, scalable device models are developed. A scalable device model, such as BSIM3, BSIM4, BSIMPD, includes model equations that comprehend a wide range of device geometrical variations and it allows the use of one set of model parameters (or a single global model card) to model devices over the range of geometrical variations. A scalable model is generally a physical model because many of its model equations are based on device physics. The global model card thus has better scalability than the binning model cards and there is no concern about discontinuity. The modeling accuracy, however, is sometimes not satisfactory, especially when it is used to comprehend relatively large devices as well as deep-submicron devices (e.g., devices with drawn channel length less than 0.1 μm or drawn channel width less than 0.13 μm), due to the complicated process and device physics associated with these smaller geometries.